Question

Expand the partial sum and find its value. $\underset{i=1}{\overset{4}{\sum {(-4)}^i}}$

Short answer

The value of the partial sum $\underset{i=1}{\overset{4}{\sum {(-4)}^i}}$is $204$

Step-by-step solution

Step 1. Given

The partial sum is$\underset{i=1}{\overset{4}{\sum {(-4)}^i}}$

To find the value of partial sum.

Step 2. Substitute the values and expand the partial sum.

Substitute the values of $i$from $1$and expand them.

$\underset{i=1}{\overset{4}{\sum {(-4)}^i=}}{(-4)}^1+{(-4)}^2+{(-4)}^3+{(-4)}^4$

Step 3. Find the values of expanded term

$$\begin{gathered} \underset{i=1}{\overset{4}{\sum {(-4)}^i}}=(-4)+16+(-64)+256 \\ =204 \end{gathered}$$

The value of partial sum is $204$